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National and Regional Contests
Switzerland Contests
Swiss NMO - geometry
2004.9
2004.9
Part of
Swiss NMO - geometry
Problems
(1)
concurrent wanted, ABCD cyclic with AB + CD = BC
Source: Switzerland - Swiss MO 2004 p9
7/19/2020
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral, so that
∣
A
B
∣
+
∣
C
D
∣
=
∣
B
C
∣
|AB| + |CD| = |BC|
∣
A
B
∣
+
∣
C
D
∣
=
∣
BC
∣
. Show that the intersection of the bisector of
∠
D
A
B
\angle DAB
∠
D
A
B
and
∠
C
D
A
\angle CDA
∠
C
D
A
lies on the side
B
C
BC
BC
.
geometry
cyclic quadrilateral
concurrent
concurrency